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ReducedTensorProduct.jl

A set of functions to work with representations in the O(3) group. In particular:

  • a module (o3) supporting implementations of irreducible representations (irreps) (irreps.jl)
  • functions to find a change-of-basis matrix Q to contract reducible representations to a single set of irreps (rtp.jl)

How to use

The file rtp.jl defines a module ReducedTensorProduct containing two functions reduced_product and reduced_product_dq, which both can be used to find Q as described above. Both can be run as serial functions or in parallel through multithreading. reduced_product_dq is the divide-and-conquer version of reduced_product and, except for very small cases, the parallelized version of reduced_product_dq is generally faster than either the serial reduced_product_dq or either version of reduced_product.

Example

include("rtp.jl")
irreps_in, irreps_out, Q = ReducedTensorProduct.reduced_product_dq("ijkl=jikl=klij", Dict('i' => "1o"), parallel=true)
# or:
irreps_in, irreps_out, Q = ReducedTensorProduct.reduced_product("ijkl=jikl=klij", Dict('i' => "1o"), parallel=false)

Benchmarking

This code was benchmarked on MIT Supercloud using the problem ijk=jik=jki with the irrep for index i being of the form 0e + 1o + 2e + .... As referenced in benchmark.csv, the parameters are

  • n: total number of CPUs
  • N: number of CPUs per node
  • l: the highest degree represented in i's irrep; l = 2 would be 0e + 1o + 2e, etc.